not really.
a side chain still is a chain. still has to store data. but i see the concept you are thinking of.
if you want to be a full node. yes you can shut down your bitcoin node and then run an angel branch/wing:aa9 node that only amounts to storing/validating 0.0244% of transactions due to there being 4096(im presuming by the aa9 hex example) branches/wings(altcoin) of angel.
what you are proposing is that Angel is becomes the 'reserve currency' like the IMF bank and each 'child' blockchain/wing is a bank branch, each with its own sortcode/routing number(aa9).
the end result is when people lock bitcoins, to play with altcoin aa9. they no longer need to run a bitcoin node and miners no longer need to mine bitcoin because they are then "spending" and protecting their value on a IMF(angel) bank branch/wing: aa9. and if that branch/wing chain is a public chain it will only be protected by the 'users' in that branch/wing. which is far LESS secure than everyone concentrating the entire hashpower on just one chain.
thus voiding hash power/difficulty away from bitcoin and then diluting that hashpower/difficulty by splitting it up into different and separate branches. because bitcoin becomes the unused leaf at the edge of the angel tree.
this idea seems a way to just push everyone onto a new ALTCOIN called angel and then technically onto many altcoins called angel:000-fff and slowly make bitcoin die when less people are playing with bitcoin due to their coins being locked.
the issue i see is that the 'branch managers' then has all the private keys to unlock the bitcoins while the customers are playing with the aa9 chain.
causing replay attacks(double spending via 2 different coins) as there needs to be a privkey somewhere to unlock coins if people wish to return.
(that issue alone of 'who/how the privkeys are managed' needs a solution, before anything else to make the concept viable)
the issue i see is that the rarity/production cap is then evaporated.
the issue i see is that users then have to trust middlemen creating new altcoins.
the issue i see is sending funds to people in different branches becomes that bit more complicated due to not transacting in just 1 chain
this essentially is a more dangerous idea than LN. because:
LN doesnt impact bitcoins security of hashpower and difficulty as much, if anything.
LN doesnt impact the rarity/deflationary production cap
as i said. all i can see is how the OP wants to 'manage' the next International monetary Fund(angel) and rule the roost, by inventing new bank branches beneath it and causing bitcoin to get down graded into just a small communities insecure credit union. because bitcoin would no longer be at the centre:
To move Bitcoin between them would involve a slow transfer back to the mainchain, and then out again to a different sidechain.
Could we instead create a protocol for addressable blockchains, all using a shared proof of work, which effectively acts as an Internet of Blockchains?
we should however be thinking about protecting and expanding bitcoin to remain 'unmanaged' by middlemen to become the new IMF, where bitcoin remains the gateway in and out of all altcoins